The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements of Projective Geometry, asserts that Desargues was the first to make use of this geometric concept.

However, inspection of the page shows that Cremona does not claim that Desargues came up with the name (in fact, the page says: "The geometric forms [...] are found, names excepted, in Desargues [...]")  . Therefore, I'm left wondering about, firstly, who did come up with this name and where. Secondly, I'm interested in the reason why this concept got the name "pencil". The name is surprising enough for me to suspect that whoever came up with it had a good reason for it. I tried to look the term up in Lo Bello's book on mathematical terminology, but there is no relevant information to be found under "pencil" in that book.

The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements of Projective Geometry, asserts that Desargues was the first to make use of this geometric concept.

However, inspection of the page shows that Cremona does not claim that Desargues came up with the name (in fact, the page says: "The geometric forms [...] are found, names excepted, in Desargues [...]"). Therefore, I'm left wondering about, firstly, who did come up with this name and where. Secondly, I'm interested in the reason why this concept got the name "pencil". The name is surprising enough for me to suspect that whoever came up with it had a good reason for it. I tried to look the term up in Lo Bello's book on mathematical terminology, but there is no relevant information to be found under "pencil" in that book.

Edit:

Has anyone ascertained whether Desargues (or Pascal) actually wrote “pencil” (or “pinceau”) — or else, who introduced the word?

The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements of Projective Geometry, asserts that Desargues was the first to make use of this geometric concept.

However, inspection of the page shows that Cremona does not claim that Desargues came up with the name (in fact, the page says: "The geometric forms [...] are found, names excepted, in Desargues [...]") . Therefore, I'm left wondering about, firstly, who did come up with this name and where. Secondly, I'm interested in the reason why this concept got the name "pencil". The name is surprising enough for me to suspect that there is a good reason for whoever came up with it had a good reason for it. I tried to look the term up in Lo Bello's book on mathematical terminology, but there is no relevant information to be found under "pencil" in that book.

The title is pretty self-explanatory: A pencil in projective (or algebraic) geometry is the family of all lines through a point. The above-linked website tells me that Cremona, on page x of Elements of Projective Geometry, asserts that Desargues was the first to make use of this geometric concept.

However, inspection of the page shows that Cremona does not claim that Desargues came up with the name (in fact, the page says: "The geometric forms [...] are found, names excepted, in Desargues [...]") . Therefore, I'm left wondering about, firstly, who did come up with this name and where. Secondly, I'm interested in the reason why this concept got the name "pencil". The name is surprising enough for me to suspect that whoever came up with it had a good reason for it. I tried to look the term up in Lo Bello's book on mathematical terminology, but there is no relevant information to be found under "pencil" in that book.